In collaboration with Kevin Hall, I have been interested in modeling how the body partitions the macronutrients of the diet into lean and fat body tissue. Using empirical cross-sectional data of the relationship between fat and lean mass, we have developed an expression for how substrate utilization adapts to changes of diet, energy expenditure, and body fat so that energy imbalances produce the observed changes of body composition. The theoretical prediction matches experimental data without the use of free parameters. We also found that if body composition follows the empirical cross-sectional curve longitudinally then the body composition in a state of energy balance is not unique but could take on an infinite number of possible values. We showed the current data is insufficient to test whether or not this prediction is true. Recently we compared the total US food supply with the estimated energy expended by the population and predicted that food waste is progressively increasing. In collaboration with Anne Sumner and Vipul Periwal, I developed a time dependent mathematical model of the suppression of lipolysis by insulin. The model can be used to develop a quantitative measure for insulin's effect on serum free fatty acids akin to insulin sensitivity for glucose. We have tested 23 possible models and used Bayesian model comparison to choose the model that best balances fit to data with minimal model complexity. We were now doing experiments to validate the model and applying it to different populations. With postdoctoral fellow Wei Huang, I have been exploring the early stages of differentiation in embryonic stem cells. We have found evidence that the changes in expression of certain genes involved in maintaining pluripotency may be reversible by the administration of different factors. A confounding problem is that the cells both proliferate as well as differentiate. Our method is to fit a growth-drift-diffusion model to the data to disentangle the two effects. We were able to estimate transition and proliferation rates that could not be obtained directly from experiments. In collaboration with Stoney Simons, former post-baccalaurete fellow Karen Ong and I developed a biophysical model for steroid-regulated gene expression in the presence of various factors. Experiments have found that factors can alter both the EC-50 and Vmax of the final product. This puts a strong constraint on the possible mechanisms. We have developed a general model involving a cascade of reactions that can predict the actions of various cofactors such as UBC-9, which is an enzyme important for sumoylation. The model may have general implications for the mechanism of gene transcription. The model shows how a sequence of reactions can yield a first order Hill function for the dose response curve between input and and output.